基于分类逻辑的函数性质研究性教学

The Research Teaching About the Properties of Functions Based on Classification Logic

函数是高等数学的主要研究对象,连续性、可导性、可微性以及可积性是高等数学的主要研究内容。但不同的函数在相应性质的研究中蕴含着不同的思维方法。文章以函数的可导性研究为例,首先利用二分法对函数进行分类——初等函数以及非初等函数,对每种情况研究过程中所运用的思维方法进行深入挖掘,引导学生在主动探索中发现知识的过程,初步体会数学知识产生过程中所蕴含的科学研究的思想和科学研究的方法,增强学员的科研意识。

Functions are the important research object of advanced mathematics,which contains the properties of continuity, derivatlve,differential and integral. There are different method and thinking according to the different function.The paper takes the derivative property as example to explore the different thinking methods in the research of elementary functions and nonelementary functions, so that the student can experience the research idea and method of the mathematicians.